Convert Between Number Bases
Instantly convert numbers between binary, decimal, hexadecimal, and octal. Essential for programmers, students, and anyone working with digital systems.
Binary, Decimal, Hex Converter
Convert numbers between binary, decimal, hexadecimal, and octal number systems in real-time.
How the Binary, Decimal, Hex Converter Works
This tool converts numbers between binary (base-2), decimal (base-10), and hexadecimal (base-16) representations. Enter a value in any format and instantly see all three representations side by side.
Conversion Process
- Enter a number in binary, decimal, or hexadecimal format
- The tool auto-detects the input format based on content and prefixes
- Binary: 0s and 1s only (optionally prefixed with 0b)
- Decimal: digits 0-9 (standard numbers)
- Hexadecimal: 0-9 and A-F (optionally prefixed with 0x)
- All three representations update simultaneously
Specific Use Cases
Programming and Debugging
A developer sees a memory address 0x7FFF in a debugger. They convert it to decimal (32,767) to understand the offset, and to binary to see the bit pattern.
Network Configuration
A network engineer works with subnet masks. Converting 255.255.255.0 to binary reveals the 11111111.11111111.11111111.00000000 pattern showing 24 network bits.
Color Code Conversion
A web designer has RGB values (255, 128, 64) and needs the hex color code. Converting each component gives #FF8040 for use in CSS.
Computer Science Education
A student learning about number systems practices conversions. They verify that binary 1010 equals decimal 10 and hex A.
Embedded Systems Development
An engineer configures hardware registers using bit masks. They convert between hex (for documentation) and binary (for understanding bit positions).
What to Know Before Using This Tool
Understanding number base systems:
- Binary (base-2): uses digits 0 and 1, fundamental to digital circuits
- Decimal (base-10): uses digits 0-9, standard human numbering
- Hexadecimal (base-16): uses 0-9 and A-F, compact representation of binary
- Each hex digit represents exactly 4 binary digits (one nibble)
- Prefixes: 0x for hex, 0b for binary (optional in this tool)
- Input is case-insensitive for hex letters (A-F or a-f)
Frequently Asked Questions
Why use hexadecimal instead of binary?
Hexadecimal is more compact and readable. One byte (8 bits) needs 8 binary digits but only 2 hex digits. Example: 11111111 = FF. It's easier to spot patterns and errors.
How do I convert binary to decimal?
Multiply each bit by its place value (powers of 2) and sum. Binary 1011 = 1×8 + 0×4 + 1×2 + 1×1 = 11 in decimal.
What does 0x mean?
"0x" is a prefix indicating hexadecimal notation. 0xFF means 255 in decimal. It helps distinguish hex from decimal numbers in code and documentation.
How many values can 8 bits represent?
8 bits (1 byte) can represent 2^8 = 256 different values, from 0 to 255. In hex, this is 0x00 to 0xFF.
What's the binary for ASCII characters?
ASCII uses 7 bits (0-127). 'A' is 65 decimal = 01000001 binary = 0x41 hex. Each character has a unique binary code used in text encoding.
Why is hex used for memory addresses?
Memory addresses are large binary numbers. Hex provides a compact, readable format. Address 0x1000 is easier to read than binary 0001000000000000 or decimal 4096.
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